Taz I do feel for your little girl; I work in a school with a bit of a similar problem.
The teachers are allowed an hours' lunchbreak. No teachers come onto the playarea during the whole hour. This is filled by teaching assistants and dinner ladies.
The morning break has a teacher on duty by the way.
As it is a special needs school, the quota of teaching assistants is quite high, on duty.
However, I do have an issue with one of the two dinner ladies. I hate to say this but she is untrained and unqualified in a teaching or teaching assistant role. When she puts away tables with a rota of helpers, the kids are often affected into the afternoon by her shouting.
I have made this problem known and it is being dealt with.
I would do the same and make sure a trained staff member, not a dinner lady is on duty. There should be staff members out on duty; make it known that they need to discreetly watch your daughter.
Personally I always make sure the kids are happy, that should be happening too on your daughter's playground.